He was a member of the Liberal Party until his preselection defeat just before the 1987 federal election, which he recontested unsuccessfully as an independent.

He was the oldest of three sons born to Margaret Ada (née Scott) and Lindsay Newton Rennie Jessop.

[2] He campaigned on better transport for rural areas and greater development of mineral resources, travelling widely in his large electorate and occasionally using an aircraft lent by a supporter.

[2] In his maiden speech, Jessop called for an independent inquiry into social security in Australia, a national superannuation scheme, the abolition of death and estate taxes, and greater federal funding for remote areas.

He was part of a group of "progressive Liberals" associated with Alan Missen who frequently crossed the floor.

[1] In June 1987, following a double dissolution, Jessop failed to win Liberal preselection for the Senate at the 1987 federal election.

He was an unsuccessful candidate on the Grey Power ticket at the 1989 South Australian state election, running for the Legislative Council.